A two player zerosum game where only one player observes a Brownian motion

Fabien Gensbittel (1) , Catherine Rainer (2)

1 GREMAQ - Groupe de recherche en économie mathématique et quantitative
2 LM - Laboratoire de mathématiques de Brest

We study a two-player zero-sum game in continuous time, where the payoff-a running cost-depends on a Brownian motion. This Brownian motion is observed in real time by one of the players. The other one observes only the actions of his opponent. We prove that the game has a value and characterize it as the largest convex subsolution of a Hamilton-Jacobi equation on the space of probability measures.

Mots clés: measure-valued process; Brownian motion; Key-words : Zero-sum continuous-time game; incomplete information; Hamilton-Jacobi equations

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Fabien Gensbittel, Catherine Rainer. A two player zerosum game where only one player observes a Brownian motion. 2016. ⟨hal-01378499v2⟩